Given: X and Y, independent, continuous uniform random variables on the interval (0,1)
Goal: Find the density function of
Use the transformation technique (as in point 5 of this wikipedia page Integration by substitution - Wikipedia, the free encyclopedia).
Define . Define .
I find that the joint density of and is
And this is where i get stuck... I tried integrating out of it but nothing reasonable comes out (not a density function anyway). So two questions:
- Did I find the joint density correct?
- I tried integrating over the interval to 1, is this correct?
- What should be next step?
Thanks for any help!